The scoreline would see the Welsh finish top of Group B as things stand, with England currently being held to a goalless draw against Slovakia in this evening's other fixture.
Chris Coleman's side started the match energetically and almost took an early lead inside the second minute when Gareth Bale's strike was parried by Russian goalkeeper Igor Akinfeev. Sam Vokes smashed in the rebound from close range, only to be denied by the offside flag.
Wales were in front less than 10 minutes later as Arsenal's Ramsey latched on to Joe Allen's measured through-pass and chipped the ball over the onrushing Akinfeev to send the Welsh supporters into a frenzy.
Things got even better for the Dragons in the 20th minute when the ball deflected into the path of an unmarked Taylor in the box and the Swansea City defender beat Akinfeev at the second time of asking.
Bale could have added a third moments before half time after beating two Russian defenders and letting fly, only to direct his effort straight at Akinfeev, and Ramsey had a goal-bound strike blocked just before the whistle.
Wales will qualify for the last 16 as Group B winners if the scorelines remain the same after 90 minutes.